On Polynomially Integrable Domains in Euclidean Spaces

Mark Agranovsky

    Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

    4 Scopus citations


    Let D be a bounded domain in ℝn, with smooth boundary. Denote VD(ω,t),ω∈Sn−1,t∈ℝ, the Radon transform of the characteristic function χD of the domain D, i.e., the (n − 1)-dimensional volume of the intersection D with the hyperplane { x∈ ℝn: < ω, x> = t}. If the domain D is an ellipsoid, then the function VD is algebraic and if, in addition, the dimension n is odd, then V (ω, t) is a polynomial with respect to t. Whether odd-dimensional ellipsoids are the only bounded smooth domains with such a property? The article is devoted to partial verification and discussion of this question.

    Original languageEnglish
    Title of host publicationTrends in Mathematics
    PublisherSpringer International Publishing
    Number of pages21
    StatePublished - 2018

    Publication series

    NameTrends in Mathematics
    ISSN (Print)2297-0215
    ISSN (Electronic)2297-024X

    Bibliographical note

    Publisher Copyright:
    © Springer International Publishing AG 2018.


    • Cross-section
    • Ellipsoid
    • Fourier transform
    • Polynomial
    • Radon transform


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